Method and device for compensating for color shift as a function of angle of view

ABSTRACT

In one embodiment of the invention, a display is provided and includes a plurality of interferometric display elements. The display further includes at least one diffuser. Optical properties of the diffuser are selected to reduce color shift of the display when viewed from at least one angle.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No.11/040,824, filed on Jan. 21, 2005, which claims the benefit of U.S.Provisional Application No. 60/613,978, filed on Sep. 27, 2004. U.S.patent application Ser. No. 11/040,824 is incorporated by reference inits entirety.

BACKGROUND

1. Field of the Invention

The field of the invention relates to microelectromechanical systems(MEMS).

2. Description of the Related Technology

Microelectromechanical systems (MEMS) include micro mechanical elements,actuators, and electronics. Micromechanical elements may be createdusing deposition, etching, and or other micromachining processes thatetch away parts of substrates and/or deposited material layers or thatadd layers to form electrical and electromechanical devices. One type ofMEMS device is called an interferometric modulator. An interferometricmodulator may comprise a pair of conductive plates, one or both of whichmay be transparent and/or reflective in whole or part and capable ofrelative motion upon application of an appropriate electrical signal.One plate may comprise a stationary layer deposited on a substrate, theother plate may comprise a metallic membrane separated from thestationary layer by an air gap. Such devices have a wide range ofapplications, and it would be beneficial in the art to utilize and/ormodify the characteristics of these types of devices so that theirfeatures can be exploited in improving existing products and creatingnew products that have not yet been developed.

SUMMARY

The system, method, and devices of the invention each have severalaspects, no single one of which is solely responsible for its desirableattributes. Without limiting the scope of this invention, its moreprominent features will now be discussed briefly. After considering thisdiscussion, and particularly after reading the section entitled“Detailed Description of Certain Embodiments” one will understand howthe features of this invention provide advantages over other displaydevices.

Another embodiment is a display that includes at least oneinterferometric modulator configured to reflect incident light. The atleast one interferometric modulator has an optical response that dependsat least in part on angle of view and wavelength of the incident light.The display further includes a diffuser positioned in an optical path tothe at least one interferometric modulator. The diffuser has an opticalresponse that is substantially matched to the optical response of theinterferometric modulator to maintain substantially the composition ofcolor at different angles of view.

Another embodiment is a display. The display includes at least oneinterferometric modulator having a spectral responsivity that varieswith angle of view, θ, such that color varies with angle of view. Thedisplay further includes a non-lambertian diffuser positioned in anoptical path to the at least one interferometric modulator. Thenon-lambertian diffuser has an optical response that varies with angleof view. The diffuser substantially reduces variation of color withangle of view.

Another embodiment is a method of fabricating a display. The methodincludes selecting a diffuser having an optical response. The methodfurther includes disposing the diffuser in front of an interferometricmodulator array. The interferometric modulator array has an opticalresponse that depends on angle of view. Selecting the diffuser includessubstantially matching the optical response of the diffuser and theoptical response of the interferometric modulator array to reduceangular color shift with angle-of-view of the display. One embodiment isa display manufactured according to this method.

Another embodiment is a method of tailoring optical properties of adisplay. The display includes an interferometric modulator having aspectral responsivity and a diffuser having an optical response. Themethod includes selecting at least one property of the diffuser withreference to the spectral responsivity of the interferometric modulatorso as to reduce color shift of the display.

Another embodiment is a display system for producing an image. Thesystem includes at least one interferometric modulator having a spectralresponsivity that depends at least in part on angle of view of thedisplay. The system further includes a diffuser positioned in at leastone optical path through the at least one interferometric modulator. Theinterferometric modulator is configured to at least partially encryptthe image from view. The diffuser is configured to decrypt the image.

One embodiment is a method of limiting view of a display to authorizedviewers. The method includes selecting at least one interferometricmodulator having a spectral responsivity that depends at least in parton angle of view of the display. The method further includes reflectinglight indicative of an image from the at least one interferometricmodulator. The interferometric modulator is configured to at leastpartially obscure the image from view. The method further comprisesdiffusing the reflected light from the at least one interferometricmodulator with a diffuser having an optical response, wherein theoptical response of the diffuser is configured to so as to decrypt theimage.

In other embodiments, other types of spatial light modulators may beused, particularly those exhibiting color shift as function of viewingposition.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an isometric view depicting a portion of one embodiment of aninterferometric modulator display in which a movable reflective layer ofa first interferometric modulator is in a released position and amovable reflective layer of a second interferometric modulator is in anactuated position.

FIG. 2 is a system block diagram illustrating one embodiment of anelectronic device incorporating a 3×3 interferometric modulator display.

FIG. 3 is a diagram of movable mirror position versus applied voltagefor one exemplary embodiment of an interferometric modulator of FIG. 1.

FIG. 4 is an illustration of a set of row and column voltages that maybe used to drive an interferometric modulator display.

FIGS. 5A and 5B illustrate one exemplary timing diagram for row andcolumn signals that may be used to write a frame of display data to the3×3 interferometric modulator display of FIG. 2.

FIG. 6A is a cross section of the device of FIG. 1.

FIG. 6B is a cross section of an alternative embodiment of aninterferometric modulator.

FIG. 6C is a cross section of another alternative embodiment of aninterferometric modulator.

FIG. 7 is a side cross-sectional view of an interferometric modulatordisplay illustrating optical paths through the modulator.

FIG. 8 schematically illustrates exemplary spectral responses R(θ_(i),λ) for different angles of incidence.

FIG. 9 is a side cross-sectional view of an interferometric modulatordisplay that includes a diffuser.

FIG. 10 is an exemplary graphical diagram of intensity versus view anglefor various diffusers.

FIG. 11 is a cross-sectional view of the interferometric modulatordisplay of FIG. 9, also showing an example of the effect of thediffuser.

FIGS. 12A and 12B are graphical diagrams illustrating the gain of anexemplary diffuser versus angle of view for light incident at twodifferent angles.

FIG. 13 is an exemplary graphical diagram of reflectance versuswavelength of light illustrating variation in spectral responsivity ofthe interferometric modulators with angle and the effects of thediffuser on the variation in spectral responsivity.

FIG. 14 is a graphical diagram of color shift versus view angleillustrating an exemplary effect of the diffuser.

DETAILED DESCRIPTION OF THE CERTAIN EMBODIMENTS

Various embodiments of the invention describe a system and method ofusing a diffuser with interferometric modulator devices so as tomitigate or compensate for color shift as a function of angle of view.In one embodiment of the invention, the display includes a plurality ofinterferometric display elements exhibiting color shift. The displayfurther includes at least one diffuser. Optical properties of thediffuser are selected to reduce color shift of the display for at leastone range of angles.

The following detailed description is directed to certain specificembodiments of the invention. However, the invention can be embodied ina multitude of different ways. In this description, reference is made tothe drawings wherein like parts are designated with like numeralsthroughout. As will be apparent from the following description, theinvention may be implemented in any device that is configured to displayan image, whether in motion (e.g., video) or stationary (e.g., stillimage), and whether textual or pictorial. More particularly, it iscontemplated that the invention may be implemented in or associated witha variety of electronic devices such as, but not limited to, mobiletelephones, wireless devices, personal data assistants (PDAs), hand-heldor portable computers, GPS receivers/navigators, cameras, MP3 players,camcorders, game consoles, wrist watches, clocks, calculators,television monitors, flat panel displays, computer monitors, autodisplays (e.g., odometer display, etc.), cockpit controls and/ordisplays, display of camera views (e.g., display of a rear view camerain a vehicle), electronic photographs, electronic billboards or signs,projectors, architectural structures, packaging, and aestheticstructures (e.g., display of images on a piece of jewelry). MEMS devicesof similar structure to those described herein can also be used innon-display applications such as in electronic switching devices.

One interferometric modulator display embodiment comprising aninterferometric MEMS display element is illustrated in FIG. 1. In thesedevices, the pixels are in either a bright or dark state. In the bright(“on” or “open”) state, the display element reflects a large portion ofincident visible light to a user. When in the dark (“off” or “closed”)state, the display element reflects little incident visible light to theuser. Depending on the embodiment, the light reflectance properties ofthe “on” and “off” states may be reversed. MEMS pixels can be configuredto reflect predominantly at selected colors, allowing for a colordisplay in addition to black and white.

FIG. 1 is an isometric view depicting two adjacent pixels in a series ofpixels of a visual display, wherein each pixel comprises a MEMSinterferometric modulator. In some embodiments, an interferometricmodulator display comprises a row/column array of these interferometricmodulators. Each interferometric modulator includes a pair of reflectivelayers positioned at a variable and controllable distance from eachother to form a resonant optical cavity with at least one variabledimension. In one embodiment, one of the reflective layers may be movedbetween two positions. In the first position, referred to herein as thereleased state, the movable layer is positioned at a relatively largedistance from a fixed partially reflective layer. In the secondposition, the movable layer is positioned more closely adjacent to thepartially reflective layer. Incident light that reflects from the twolayers interferes constructively or destructively depending on theposition of the movable reflective layer, producing either an overallreflective or non-reflective state for each pixel.

The depicted portion of the pixel array in FIG. 1 includes two adjacentinterferometric modulators 12 a and 12 b. In the interferometricmodulator 12 a on the left, a movable and highly reflective layer 14 ais illustrated in a released position at a predetermined distance from afixed partially reflective layer 16 a. In the interferometric modulator12 b on the right, the movable highly reflective layer 14 b isillustrated in an actuated position adjacent to the fixed partiallyreflective layer 16 b.

The fixed layers 16 a, 16 b are electrically conductive, partiallytransparent and partially reflective, and may be fabricated, forexample, by depositing one or more layers each of chromium andindium-tin-oxide onto a transparent substrate 20. The layers arepatterned into parallel strips, and may form row electrodes in a displaydevice as described further below. The movable layers 14 a, 14 b may beformed as a series of parallel strips of a deposited metal layer orlayers (orthogonal to the row electrodes 16 a, 16 b) deposited on top ofposts 18 and an intervening sacrificial material deposited between theposts 18. When the sacrificial material is etched away, the deformablemetal layers are separated from the fixed metal layers by a defined airgap 19. A highly conductive and reflective material such as aluminum maybe used for the deformable layers, and these strips may form columnelectrodes in a display device.

With no applied voltage, the cavity 19 remains between the layers 14 a,16 a and the deformable layer is in a mechanically relaxed state asillustrated by the pixel 12 a in FIG. 1. However, when a potentialdifference is applied to a selected row and column, the capacitor formedat the intersection of the row and column electrodes at thecorresponding pixel becomes charged, and electrostatic forces pull theelectrodes together. If the voltage is high enough, the movable layer isdeformed and is forced against the fixed layer (a dielectric materialwhich is not illustrated in this Figure may be deposited on the fixedlayer to prevent shorting and control the separation distance) asillustrated by the pixel 12 b on the right in FIG. 1. The behavior isthe same regardless of the polarity of the applied potential difference.In this way, row/column actuation that can control the reflective vs.non-reflective pixel states is analogous in many ways to that used inconventional LCD and other display technologies.

FIGS. 2 through 5 illustrate one exemplary process and system for usingan array of interferometric modulators in a display application. FIG. 2is a system block diagram illustrating one embodiment of an electronicdevice that may incorporate aspects of the invention. In the exemplaryembodiment, the electronic device includes a processor 21 which may beany general purpose single- or multi-chip microprocessor such as an ARM,Pentium®, Pentium II®, Pentium III®, Pentium IV®, Pentium® Pro, an 8051,a MIPS®, a Power PC®, an ALPHA®, or any special purpose microprocessorsuch as a digital signal processor, microcontroller, or a programmablegate array. As is conventional in the art, the processor 21 may beconfigured to execute one or more software modules. In addition toexecuting an operating system, the processor may be configured toexecute one or more software applications, including a web browser, atelephone application, an email program, or any other softwareapplication.

In one embodiment, the processor 21 is also configured to communicatewith an array controller 22. In one embodiment, the array controller 22includes a row driver circuit 24 and a column driver circuit 26 thatprovide signals to a pixel array 30. The cross section of the arrayillustrated in FIG. 1 is shown by the lines 1-1 in FIG. 2. For MEMSinterferometric modulators, the row/column actuation protocol may takeadvantage of a hysteresis property of these devices illustrated in FIG.3. It may require, for example, a 10 volt potential difference to causea movable layer to deform from the released state to the actuated state.However, when the voltage is reduced from that value, the movable layermaintains its state as the voltage drops back below 10 volts. In theexemplary embodiment of FIG. 3, the movable layer does not releasecompletely until the voltage drops below 2 volts. There is thus a rangeof voltage, about 3 to 7 V in the example illustrated in FIG. 3, wherethere exists a window of applied voltage within which the device isstable in either the released or actuated state. This is referred toherein as the “hysteresis window” or “stability window.” For a displayarray having the hysteresis characteristics of FIG. 3, the row/columnactuation protocol can be designed such that during row strobing, pixelsin the strobed row that are to be actuated are exposed to a voltagedifference of about 10 volts, and pixels that are to be released areexposed to a voltage difference of close to zero volts. After thestrobe, the pixels are exposed to a steady state voltage difference ofabout 5 volts such that they remain in whatever state the row strobe putthem in. After being written, each pixel sees a potential differencewithin the “stability window” of 3-7 volts in this example. This featuremakes the pixel design illustrated in FIG. 1 stable under the sameapplied voltage conditions in either an actuated or releasedpre-existing state. Since each pixel of the interferometric modulator,whether in the actuated or released state, is essentially a capacitorformed by the fixed and moving reflective layers, this stable state canbe held at a voltage within the hysteresis window with almost no powerdissipation. Essentially no current flows into the pixel if the appliedpotential is fixed.

In typical applications, a display frame may be created by asserting theset of column electrodes in accordance with the desired set of actuatedpixels in the first row. A row pulse is then applied to the row 1electrode, actuating the pixels corresponding to the asserted columnlines. The asserted set of column electrodes is then changed tocorrespond to the desired set of actuated pixels in the second row. Apulse is then applied to the row 2 electrode, actuating the appropriatepixels in row 2 in accordance with the asserted column electrodes. Therow 1 pixels are unaffected by the row 2 pulse, and remain in the statethey were set to during the row 1 pulse. This may be repeated for theentire series of rows in a sequential fashion to produce the frame.Generally, the frames are refreshed and/or updated with new display databy continually repeating this process at some desired number of framesper second. A wide variety of protocols for driving row and columnelectrodes of pixel arrays to produce display frames are also well knownand may be used in conjunction with the present invention.

FIGS. 4 and 5 illustrate one possible actuation protocol for creating adisplay frame on the 3×3 array of FIG. 2. FIG. 4 illustrates a possibleset of column and row voltage levels that may be used for pixelsexhibiting the hysteresis curves of FIG. 3. In the FIG. 4 embodiment,actuating a pixel involves setting the appropriate column to −V_(bias),and the appropriate row to +ΔV, which may correspond to −5 volts and +5volts respectively Releasing the pixel is accomplished by setting theappropriate column to +V_(bias), and the appropriate row to the same+ΔV, producing a zero volt potential difference across the pixel. Inthose rows where the row voltage is held at zero volts, the pixels arestable in whatever state they were originally in, regardless of whetherthe column is at +V_(bias), or −V_(bias).

FIG. 5B is a timing diagram showing a series of row and column signalsapplied to the 3×3 array of FIG. 2 which will result in the displayarrangement illustrated in FIG. 5A, where actuated pixels arenon-reflective. Prior to writing the frame illustrated in FIG. 5A, thepixels can be in any state, and in this example, all the rows are at 0volts, and all the columns are at +5 volts. With these applied voltages,all pixels are stable in their existing actuated or released states.

In the FIG. 5A frame, pixels (1,1), (1,2), (2,2), (3,2) and (3,3) areactuated. To accomplish this, during a “line time” for row 1, columns 1and 2 are set to −5 volts, and column 3 is set to +5 volts. This doesnot change the state of any pixels, because all the pixels remain in the3-7 volt stability window. Row 1 is then strobed with a pulse that goesfrom 0, up to 5 volts, and back to zero. This actuates the (1,1) and(1,2) pixels and releases the (1,3) pixel. No other pixels in the arrayare affected. To set row 2 as desired, column 2 is set to −5 volts, andcolumns 1 and 3 are set to +5 volts. The same strobe applied to row 2will then actuate pixel (2,2) and release pixels (2,1) and (2,3). Again,no other pixels of the array are affected. Row 3 is similarly set bysetting columns 2 and 3 to −5 volts, and column 1 to +5 volts. The row 3strobe sets the row 3 pixels as shown in FIG. 5A. After writing theframe, the row potentials are zero, and the column potentials can remainat either +5 or −5 volts, and the display is then stable in thearrangement of FIG. 5A. It will be appreciated that the same procedurecan be employed for arrays of dozens or hundreds of rows and columns. Itwill also be appreciated that the timing, sequence, and levels ofvoltages used to perform row and column actuation can be varied widelywithin the general principles outlined above, and the above example isexemplary only, and any actuation voltage method can be used with thepresent invention.

The details of the structure of interferometric modulators that operatein accordance with the principles set forth above may vary widely. Forexample, FIGS. 6A-6C illustrate three different embodiments of themoving mirror structure. FIG. 6A is a cross section of the embodiment ofFIG. 1, where a strip of metal material 14 is deposited on orthogonallyextending supports 18. In FIG. 6B, the moveable reflective material 14is attached to supports at the corners only, on tethers 32. In FIG. 6C,the moveable reflective material 14 is suspended from a deformable layer34. This embodiment has benefits because the structural design andmaterials used for the reflective material 14 can be optimized withrespect to the optical properties, and the structural design andmaterials used for the deformable layer 34 can be optimized with respectto desired mechanical properties. The production of various types ofinterferometric devices is described in a variety of publisheddocuments, including, for example, U.S. Published Application2004/0051929. A wide variety of well known techniques may be used toproduce the above described structures involving a series of materialdeposition, patterning, and etching steps.

FIG. 7 is a side cross-sectional view of an interferometric modulator 12illustrating optical paths through the modulator 12. The color of lightreflected from the interferometric modulator 12 may vary for differentangles of incidence (and reflection) as illustrated in FIG. 7. Forexample, for the interferometric modulator 12 shown in FIG. 7, as lighttravels along path A₁, the light is incident on the interferometricmodulator at a first angle, reflects from the interferometric modulator,and travels to a viewer. The viewer perceives a first color when thelight reaches the viewer as a result of optical interference between apair of minors in the interferometric modulator 12. When the viewermoves or changes his/her location and thus view angle, the lightreceived by the viewer travels along a different path A₂ havingcorresponding a second different angle of incident (and reflection).Optical interference in the interferometric modulator 12 depends onoptical path length of light propagated within the modulator. Differentoptical path lengths for the different optical paths A₁ and A₂ thereforeyield different outputs from the interferometric modulator 12. The usertherefore perceives different colors depending on his or her angle ofview. This phenomenon is referred to as a “color shift”.

The amount of color shift may be expressed in terms of a difference inwavelength, e.g., in nanometers, for the light emitted from theinterferometric modulators for different angles of incident (andreflected light). As is well known, for spectral reflection, the angleof incidence is equal to the angle of reflection. The wavelength used tomeasure the color shift may be the peak wavelength of the speculardistribution of light output from the interferometric modulator. As usedto herein, specular distribution refers to the wavelength distribution,such as for example, the intensity of light at different wavelengths.

The output of the interferometric modulator 12 may be characterized by aspectral responsivity function or spectral response R(θ_(i), λ), whereθ_(i) is the angle of incidence of light and λ is the wavelength. Asdescribed above, the spectral output of the interferometric modulator 12varies with angle of incidence (and angle of reflection). FIG. 8schematically illustrates exemplary spectral responses R(θ_(i), λ) fordifferent angles of incidence. A first plot 110, for example, shows aspectral response (output versus wavelength) for a first angle ofincidence. A second plot 120 shows a spectral response for a secondangle of incidence. The first and second plots each have peaks 115, 125,sometime referred to herein as spectral lines. These plots 110, 120 andthe corresponding peaks are shifted from each other. The shift in thepeaks 115, 125 for the different plots shows the color shift with angleof view.

Generally, a certain amount of perceived off-axis color shift in adisplay may be tolerated for certain displays. A color shift or achange, e.g., of about 5-30 nanometers in wavelength for an angle ofview shift of about 40° may be acceptable for certain applications.However, in some cases, the color shift is too significant and isnoticeable by the observer. In such a case, methods of correcting orcompensating for such intolerable color shifts as described herein maybe employed. In practice, the level of tolerance that is permissible maydepend upon factors that include the intended use of the display, thequality, and/or the price range of the display. As indicated above, thelevel of “tolerance” in color shift may be expressed in terms ofnanometers of wavelength shift for a change in view angle of a specifiedrange. For example, in one embodiment, the tolerance may be expressedfor a range between about −60° and 60°. In another embodiment, forexample, a display used as part of signage, the tolerance may beexpressed for a range between about −80° and 80°.

In certain preferred embodiments, a diffuser may be used to compensatefor the color shift of an interferometric modulator structure. FIG. 9shows one embodiment of interferometric modulator display 200 thatincludes a diffuser layer 201. The interferometric modulator display 200includes a transparent substrate 20, such as glass, having a viewingsurface to which the diffuser layer 201 is attached. In one embodiment,for example, the diffuser layer 201 is formed on the top side of thesubstrate 20 as shown in FIG. 9. Other designs are also possible.

Diffusers may comprise bulk diffuser material. For example, a diffusermay include one or more layers of a material such as a suitabletransparent or translucent polymer resin, for example, polyester,polycarbonate, polyvinyl chloride (PVC), polyvinylidene chloride,polystyrene, polyacrylates, polyethylene terephthalate, polyurethane,and copolymers or blends thereof. Other materials may be employed aswell.

In one embodiment, the diffuser is attached to a surface of thesubstrate using a double-sided adhesive.

FIG. 10 is a graphical diagram 300 of exemplary optical responses,referred to as D(θ_(i), θ), for a diffuser or diffuser material inaccordance embodiments of the invention. Output from the diffuser maydepend on both angle of incidence θ_(i) and on angle of transmission orangle of view, θ. Accordingly, the optical transfer function D(θ_(i), θ)may be expressed as a function of the angle of view “θ” and the angle ofincidence of light “θ_(i)” ranging, e.g., from 0 to 90° or from 0 to−90°.

As shown in FIG. 10, the vertical axis depicts the relative intensity oflight from a light source that is observed through a diffuser. Thehorizontal axis represents the angle of viewing of light communicatedthrough the diffuser. The possible angle of view varies from 0 to 90degrees on the right side of graph and from 0 to −90 degrees-left sideof graph 300).

Curves or traces 310, 320, and 330 in FIG. 10 depict the opticalresponse of diffusers for a given angle of incidence, θ_(i) as theoutput varies with transmission angle or view angle θ. This angle ofincidence may, for example, be 0° for the plots 310, 320, 330 in FIG.10. The plots 310, 320, 330 in FIG. 10 show how much light is outputfrom the diffuser in different directions corresponding to differentangles of view, θ. For example, D(θ_(i),0° corresponds to the value ofθ=0° in FIG. 10.

As further shown in FIG. 10, the first trace 310 depicts the perceivedintensity of light versus angle of viewing for a particular diffuser(and a particular angle of incidence). In one embodiment, the trace 310has a generally a bell-shaped curve that has a relatively sharp peak ata center angle. The sharp or relatively narrow peak is located at 0° forthis embodiment of the diffuser. This narrow peak may for example have awidth as measured at full width half maximum of about 10-30°. This typeof trace is sometimes referred to as a high gain curve.

The trace 320 depicts an optical response for a second type of diffuser.The trace 320 is a generally bell-shaped curve that has a relativelysmall wider peak at its center. This narrow peak may for example have awidth as measured at full width half maximum of about 60-100° The trace320, with its relatively low peak and thus somewhat flattened responseprofile is sometimes referred to as a low gain curve. As shown inconnection with the traces 310 and 320, each optical response is shownas centered at about 0° for the purpose of illustration. As will bediscussed further below, the optical response may be centered at otherangles for different diffusers.

Finally, FIG. 10 shows a trace 330 depicting the optical response of anideal Lambertian diffuser. Lambertian diffusers are characterized by asubstantially flat angular response profile. Thus, the trace 330 depictsan approximately straight line response having a generally fixedintensity at all angles of viewing. Conversely, non-lambertian diffusersdo not have substantially flat angular response profiles. The high gainand low gain diffusers corresponding to traces 310 and 320 are examplesof non-lambertian diffusers.

As discussed above, the traces 310 and 320 illustrate optical responsesof various diffusers having responses that are centered around zerodegrees (0°). In other embodiments, similar shaped (or other shaped)response profiles may be centered on view angles other than zerodegrees, such as, for example, at ten (10), twenty (20), thirty (30),forty (40), 45 (forty five), 50 (fifty), 60 (sixty), 70 (seventy), 80(eighty) degrees, or on any other view angle.

Accordingly, D(θ_(i), θ) may be characterized by a response profile thatmay be different characteristically for different angles of view. Invarious embodiments, for example, the diffuser 201 may be a high gain,low gain (or very low gain), or any other suitable type of diffusertherebetween, or any combination thereof. As will be apparent from thefollowing discussion, the centering of D(θ_(i), θ) around a particularangle is relevant to computing a convolution of D(θ_(i), θ) and opticalresponse of the interferometric modulator, without the diffuser, whichis referred to as R(θ_(i), λ).

FIG. 11 is a cross-sectional view illustrating an embodiment of aninterferometric modulator display 400 that includes a diffuser 402. Inone embodiment, the display 400 includes an array of interferometricmodulators 401. In certain embodiments, the diffuser 402 is physicallycoupled to a substrate 403. Light is reflected in the interferometricmodulator 401 so as to pass outward through the diffuser 402. Asdescribed in further detail below, the diffuser 402 is selected based onits characteristics which influence the reflected light so as tocompensate for at least a portion of the angular color shift of theinterferometric modulator 401. This compensation reduces the perceivedcolor shift as the viewing angle of a user of the modulator 401 changes.In operation, light from the light source (not shown) is incident on themodulator 401 along optical paths such as exemplary paths 410, 412, and414. Light on the exemplary optical paths 410, 412, and 414 is incidentat angles of, e.g., 20, 30, and 40 degrees. It is to be recognized thatany numerical values used herein, such as the angles of incidence oflight paths 410, 412, and 414, are presented for purposes ofillustration and are not necessarily indicative of any embodiment.

The modulator 401 reflects the light further along the paths 410, 412,and 414. The light along the paths 410, 412, and 414 is then incident onthe diffuser 402. The diffuser 402 redirects portions of the reflectedlight along a range of optical paths at intensities that depend upon thegain characteristics, D(θ_(i), θ), of the diffuser 402. The diffusedportion of the light from optical paths 410, 412, and 414, travels to aviewing position along optical paths 416. These paths 416 are atsubstantially the same angle with respect to the diffuser 402 andsubstantially parallel for this particular exemplary viewing position430 which is a distant viewing position.

The diffuser 402 thus operates to collect light that is incident on themodulator 401 at a range of angles and corresponding optical paths,including the paths 410, 412, and 414. This collected light isredirected. A portion of this light is redirected to the viewingposition along the optical paths 416.

The diffuser 402 thus collects light from the modulator 401 (or array ofmodulators 401) at a range of wavelengths to produce a net opticalresponse for the modulator 401 as modified by the diffuser 402. The netoptical response is related to the convolution of the optical responseD(θ_(i), θ) of the diffuser with the optical response R(θ_(i), λ) of themodulator 401 over a range of angles of light incident on the display400.

By controlling the characteristics, e.g., D(θ_(i), θ), of the diffuser402 in conjunction with optical response of the modulator 401, the netoptical response of the system 400 can thus be controlled to achieve adesired net optical response. In one embodiment, the characteristics ofthe diffuser 402 and the interferometric modulator 401 are selected soas to substantially compensate for angular color shift of theinterferometric modulator 401. In another embodiment, thecharacteristics of the diffuser 402 and the modulator 401 are selectedso that an image formed by the modulator array alone is obscured orencrypted and is not visible. The image formed by the modulator array,however, is visible by viewing through the diffuser 402.

The overall optical characteristics of the modulator 401 together withthe diffuser 402 may be modeled in terms of the convolution of theoptical response (i.e., spectral reflectance or transfer function) ofthe modulator 401, with the optical response of the diffuser 402. Anexemplary expression for this convolution is set forth below.

As noted above, the optical response R(θ_(i),λ) of the modulator 401 isrepresented as a function of the angle of incidence, θ_(i), andwavelength of light, λ, entering the modulator 401. As the angle ofincidence is equal to the angle of reflection for specular reflection,the view angle, θ, for the modulator is equal to the angle of incidence,θ_(i), on the modulator. Hence, R(θ_(i),λ) characterizes the opticalresponse of the modulator as a function of view angle, θ.

The intensity of the light coming out of the diffuser 402 is alsogenerally a function of the viewing angle θ (and angle of incidenceθ_(i)). Accordingly, as described above, the optical response of thediffuser is characterized by D(θ_(i), θ).

For the combination of the modulator 401 and the diffuser 402, the viewangle, θ, of the modulator corresponds to the angle of incidence, θ_(i),of the diffuser. Thus, the total or net optical response of themodulator 401 as modified by the diffuser 402 (see FIG. 11) may beexpressed as R′(θ,λ) in accordance with the following relation:

${R^{\prime}\left( {\theta,\lambda} \right)} = {\sum\limits_{\theta_{i}}{{D\left( {\theta_{i},\theta} \right)}{R\left( {\theta_{i},\lambda} \right)}}}$

Using the above equation, the modified spectral reflectance R′(θ,λ) thatincludes the effects of the diffuser 402 can be computed. The summationis performed for a range of angles θ_(i) (i.e., for θ_(i)=0 to 90degrees) in determining the responsivity R′(θ,λ). The result is spectralresponse of the display for a given view angle θ.

The spectral response of the combination of the modulator 401 and thediffuser 402 can thus be computed for a particular viewing angle andcorresponding viewer position. Similarly, the spectral response for theaggregate structure comprising the modulator 401 and the diffuser 402may be computed for multiple viewing angles and view positions toquantify color shift resulting from change in angle of view.

In one embodiment, it is desirable to define the type of overall orcorrected reflectance (i.e., R′(θ,λ)) in terms of particular criteria,e.g., acceptable or unacceptable level of color shift. For example, ifthe color shift at a particular angle of view (e.g., 30 degrees) is 100nanometers, it may be desirable to reduce such color shift to no morethan 20 nanometers. In such a case, the uncompensated optical responseR(θ_(i),λ) of the modulator 401 having an undesirable 100-nanometercolor shift (e.g., at 30 degrees) may be improved with a suitablediffuser so as to provide a resultant spectral response R′(θ,λ)) havingan acceptable 20-nanometer color shift. It is worth noting that thesenumbers are chosen arbitrarily for illustrative purpose, and anytolerance level in color shift may be used in practice. For instance incertain embodiments, the level of tolerance in color shiftcharacteristics may depend on intended use or planned viewingconditions.

Accordingly, the desirable optical response R′(θ,λ) is derivable fromthe uncompensated optical response R(θ_(i),λ). In this case, since theoptical response of uncompensated R(θ_(i),λ) and desired R′(θ_(i),θ) areknown functions, the optical response (i.e., characteristics) forD(θ_(i), θ) can be computed from the above equation. Since the aboveequation has only one unknown variable, D(θ_(i), θ) can be determined todefine the suitable diffuser for providing the desired spectralresponsivity R′(θ,λ). The D(θ_(i), θ), once solved may, for example,correspond to a diffuser having a high gain, a low gain, or a very lowgain response, or other suitable characteristics.

In one embodiment, D(θ_(i), θ) is determined by solving permutations ofthe equation above (e.g., solving the deconvolution). Well knownmathematical and numerical methods may be employed to perform thecalculations.

As is well known in the art, diffusers may be fabricated to provide adesired optical response. Accordingly, once characteristics ofD(θ_(i),θ) are determined, a suitable physical configuration andmaterial of the diffuser 402 may then be determined to produce at leastan approximation of the desired response profile D(θ_(i),θ) such thatthe color shift is within a desired tolerance at the target angle. Invarious embodiments, the physical configuration may be determined usingtechniques such as are known in the art. Diffusers with selectedproperties are available, for example, from Nitto Denko, Osaka, Japan.Additional details regarding selecting a diffuser based on the spectralresponse of the interferometric modulator are discussed more fullybelow.

To illustrate application of this optical model, calculations fordetermining the spectral response R′(θ,λ) of the combination of themodulator 401 and diffuser 402 based on the known spectral responseR(θ_(i),λ) of the modulator 401 and the known optical responseD(θ_(i),θ) of the diffuser are provided.

In one embodiment, for example, the diffuser 402 is a diffuser havinghigh gain characteristics that may be selected to reduce or compensatefor the color shift. FIG. 12A is a graphical diagram illustrating thegain of the exemplary diffuser 402 versus angle of view for an angle ofincidence of 0°. FIG. 12B is a graphical diagram illustrating the gainof the exemplary diffuser 402 versus angle of view at an angle ofincidence of 10°. In this illustration, it may be assumed that thefollowing values for R(θ_(i), λ) are derived from the curve of theoptical response (not shown):

${R\left( {{0{^\circ}},\lambda} \right)} = \begin{bmatrix}0.5 \\0.9\end{bmatrix}$ and${R\left( {{10{^\circ}},\lambda} \right)} = \begin{bmatrix}0.6 \\0.8\end{bmatrix}$

In this example, the calculations are illustrated using only two anglesof incidence for a single wavelength, are provided. In particular, theconvolution is calculated for angle of incidence ranging from 0 to 10°with a step size of 10°. In practice, a larger range of angles may beused and the step size may be different. Likewise, it is to beunderstood that, values for various wavelengths may be identified at anyparticular angle of incidence (or angle of view); in this example, only0° and 10° are being used.

Also, there are many different wavelengths at each angle of view;however only two values (0.5 and 0.9) for the wavelength, λ, areprovided at 0 degrees (angle of incidence θ_(i) or angle of view) forillustration only. Similarly, two values (0.6 and 0.8) for thewavelength, λ, are provided at an angle of view of 10 degrees.

To verify that the selected diffuser 402 performs the intended colorshift compensation, for example, one may compute R′(θ,λ) using theactual optical response D(θ_(i), θ) of the diffuser 402. To determinesuch compensated optical response R′(θ,λ) of the modulator 401 asmodified by the diffuser 402, the equation above is used to computeR′(θ,λ) at a desired angle of view. In this example, the opticalresponse D(θ_(i), θ) is used and it is assumed that D(0°, 10°)=0.5 andD(10°, 10°)=0.2 to compute the effect of the diffuser 402 at an angle ofview 10°. It is to be recognized that these numbers have been selectedarbitrarily to illustrate the principle described herein and are notlimiting. Moreover, as discussed above, the convolution may be performedfor a greater number of angles of incidence θ_(i), even though in thisnumeric example only values at two values of θ_(i) are provided forD(θ_(i), θ), i.e., 0.2 and 0.5.

In performing the convolution of D(θ_(i), θ) with R(θ_(i), λ), R′(θ,λ)can be computed at an angle of view of 10° (or at any desired angle ofview, e.g., between 0° and 90°, in a like manner). In performing theconvolution in this particular example, each value for D(θ_(i), θ) thatis used is obtained from the D(θ_(i), θ) curve at the angle of view (inthis example, θ=10°) for all values of θ_(i).

As noted above, for each angle of view computation, the convolution issummed by varying θ_(i) from 0° to 90° to compute the total modified orcompensated optical response R′(θ,λ) (as corrected by the diffuser 402).In this numeric example, the computation may operate as follows:

$\begin{matrix}{{R^{\prime}\left( {{10{^\circ}},\lambda} \right)} = {{{D\left( {{0{^\circ}},{10{^\circ}}} \right)}*{R\left( {{0{^\circ}},\lambda} \right)}} + {{D\left( {{10{^\circ}},{10{^\circ}}} \right)}*{R\left( {{10{^\circ}},\lambda} \right)}}}} \\{= {{\lbrack 0.50\rbrack*\begin{bmatrix}0.5 \\0.9\end{bmatrix}} + {\lbrack 0.20\rbrack*\begin{bmatrix}0.6 \\0.8\end{bmatrix}}}} \\{= {\begin{bmatrix}0.25 \\0.45\end{bmatrix} + \begin{bmatrix}0.12 \\0.16\end{bmatrix}}} \\{= \begin{bmatrix}0.37 \\0.61\end{bmatrix}}\end{matrix}$

In some embodiments, the diffuser 402 may include more than one diffuserlayer. In one such embodiment, the same diffuser characteristics may beselected for each of the diffuser layers. In another embodiment,different characteristics may be selected for each of the layers of thediffuser 402. In one embodiment, the diffuser characteristics of thediffuser 402 may be calculated by convolving the optical responses ofeach of the layers.

FIG. 13 illustrates a graphical diagram 500 of several spectralreflectance traces for various configurations of interferometricmodulator display devices. As shown in FIG. 13, the vertical axisrepresents a reflectance to the viewer, expressed as a percentage (from0 to 90%). The horizontal axis represents the wavelength of light thatis reflected by the interferometric modulator. This reflectancecorresponds to the spectral responsivity e.g., R(θ_(i), λ), R′(θ,λ),described above.

As further shown in FIG. 13, curve 510 depicts a somewhat bell-shapedcurve that represents the reflectance as viewed at 0 degrees to normalfrom the display of one or more interferometric modulators (without thepresence of a diffuser layer). The peak of curve 510 is at approximately80% reflectance and is centered about 820 nm, which is in the infraredportion of the spectrum.

FIG. 13 further depicts a curve 520 that represents the reflectance ofthis same display as viewed at 50 degrees to normal. The curve 520 isshaped similarly to the curve 510 but has a peak value of reflectance ofapproximately 84% that is located at about 690 nm.

FIG. 13 also depicts a somewhat bell-shaped curve 530 that representsthe reflectance as viewed at 0 degrees to normal from a display thatincludes a diffuser layer. The curve 530 has a peak gain ofapproximately 64% that is located approximately at 750 nm. FIG. 13depicts a curve 540 that represents the reflectance of the displayhaving the diffuser layer as viewed at 50 degrees to normal. The curve540 follows a path that is substantially the same as the path of curve530 with a slightly smaller peak reflectance value of 62%.

FIG. 13 shows the reflectance from the modulator using input light tothe interferometric modulator that is in the infrared portion of theelectromagnetic spectrum at about a peak wavelength of 810 nanometers(nm). As can be seen by comparing the curves 510 and 530 to each other,the 50 degree shift in viewing angle causes an approximately 120 nmcolor shift in the viewed response profile. The curves 530 and 540illustrate the spectral reflectance of the modulator when viewed througha very low gain diffuser 302 having a full width half maximum gainbetween 120° and 180°. Mathematically, the curves 530 and 540 representthe convolution of the response of this very low gain diffuser with thatof the interferometric modulator. As shown in FIG. 13, both curves 530and 540 peak at about the same or a similar wavelength that ishorizontally between the peaks of curves 510 and 520. The curves thusexhibit a very minor perceived color shift (such as in the range ofabout 10 to 20 nm) when the viewing angle changes by fifty degrees)(50°, as in this example.

As compared to the 120 nm color shift of the modulator viewed at 50°without the diffuser layer, the diffuser layer has thus beensubstantially compensated for the shift in viewing angle. The peaks ofthe curves 530 and 540 do not shift in color substantially with changingviewing angle.

Additionally, the peaks of curves for the modulator without the diffuserthat were in the infrared portion of the spectrum are in the red portionof the spectrum with the low gain diffuser. The diffuser has thereforeshifted the spectral responsivity of an interferometric modulator have apeak response in the infrared to a device having a peak in a visiblewavelength. Another characteristic of the effect of the diffuser is thatthe peak spectral reflectance of the convoluted, e.g., perceived, lightsignal is reduced and spread more evenly across the spectrum.

The color shift and the amount of the drop in peak reflectance may becontrolled by selecting the desired wavelength and angle for the peak ofthe curve for a diffuser. In one embodiment, the selected diffuser mayhave a response that is centered about 0°. In other embodiments, theselected diffuser may have a response centered around an angle otherthan 0°, for example, centered at ten)(10°), twenty (20), thirty (30),forty (40), 45 (forty five), 50 (fifty), 60 (sixty), 70 (seventy), 80(eighty) degrees, or on any other view angle.

FIG. 14, is a CIE 1976 chromaticity diagram 600 that illustrates asequence of data points that show color shift versus view angle tofurther illustrate the effect of the embodiment of the diffuser 401 fromFIG. 13. The horizontal and vertical axes define a chromaticitycoordinate system on which spectral tri-stimulus values may be depicted.A sequence of data points for an interferometric modulator displaywithout diffuser is shown on the gamut color space of the diagram alonga trace 605. The curve of the trace 605 indicates that there is aconsiderable color shift for changes in the view angle. For theinterferometric modulator display with the very low gain response, suchas shown in traces 530 and 540 of FIG. 13, a single data point 610 isshown on the diagram 401 because the color shift has been substantiallyeliminated by use of the diffuser layer

More generally, a diffuser can be selected having specific propertiesthat produce a desired spectral responsivity, R′(θ,λ). Examples ofproperties that can be varied include the shape of the optical responseD(θ_(i), θ). As discussed above, the diffuser may comprise, e.g., anon-lambertian diffuser such as a high gain, low gain, or very low gaindiffuser. In the case where the optical response D(θ_(i), θ) comprises apeak, the width of this peak can be selected. For example, peaks asmeasured at full width half maximum may be between about 2° to 20° widein some embodiments or between about 20° to 120° wide or larger orsmaller. Peaks widths outside these ranges are also possible. Inaddition, the position of this peak can be controlled. Although the highand low gain response shown in FIG. 10 are centered about 0°, in certainembodiments, diffusers having peaked optical response with peak atlocations other than 0° may be used. Other properties of the diffusermay be varied as well.

For example, the optical responses depicted in FIG. 10 are for aparticular angle of incidence; however, D(θ_(i), θ) is also a functionof θ_(i). In various embodiments, therefore, the diffuser may beconfigured to provide different optical responses D(θ) for lightincident at different angles of incidence θ_(i). For example, thediffuser may be designed such that the width and location of peaks inthe optical response are different for differing angles of incidence.The peak may for example be located at an angle of view equal (butopposite) to the angle of incidence. Alternatively, the angle of view ofthe peak may be different in magnitude from the angle of incidence.

Since the spectral responsivity of the interferometric modulator varieswith angle, different responses for different angles of incidence may beemployed to redistribute the rays to achieve the desired dependency ofcolor on view angle. Accordingly, reduced color shift may be achieved byproperly distributing the light incident on the diffuser at differentangles.

Thus, by selecting the different features of the optical responseD(θ_(i), θ), the desired spectral responsivity R′(θ,λ) may be obtained.Consideration of the spectral responsivity R(θ_(i), λ) of theinterferometric modulator may be used in determining the properties ofsuch a suitable diffuser. Accordingly, a diffuser may be selected thatappropriately matches the interferometric modulator so as, for example,to reduce color shift.

As described above, using techniques known in the art, the selectionand/or design of the diffuser may be based on the known spectral andangular optical response of diffuser materials and architectures. Inparticular, the diffuser is selected or designed so that the convolutionof the diffuser's optical response with that of the interferometricmodulator 401 produces an optical response that decreases the colorshift. Thus, the color shift as viewed from at least one target anglemay be reduced to within a predetermined tolerance for a particularviewing angle and particular interferometric modulator configuration401. The predetermined tolerance may be expressed as a number ofnanometers of color shift.

Holographic or diffractive optical elements may be employed as thediffuser. The diffusers may also be computer generated. In oneembodiment, the desired optical response for the diffuser is produced byselecting materials, thicknesses, and arrangement of the materials ofthe diffuser to produce the desired optical response for the diffuser.

In certain embodiments, the interferometric modulator has a spectralresponse (e.g., for viewing angles at normal incidence) that is centeredin the infrared or other non-visible wavelength. Such a spectralresponse having mostly non-visible components may contribute to reducedcolor shifting. For example 50%, 60%, 70% or more of the wavelengthsunder a central peak that extends in the visible may be non-visible. Thediffuser may shift this peak into the visible.

In certain embodiments, the diffuser may exhibit a response D(θ_(i), θ,λ) that is a function of wavelength. In one embodiment, the diffuserincludes a holographic optical element. Other types of wavelengthsensitive diffusers may be employed as well.

In addition, in embodiments where a shift to the blue end of thespectrum is desired, a back light or front light may be added to provideadditional intensity at desired wavelengths. The use of such frequencydependent diffuser configurations and light sources provides additionalflexibility in selecting a configuration that may be viewed at aselected angle with a predetermined tolerance on color shift.

In one embodiment, the display 400 may include interferometricmodulators 401 that have varying optical responses. For example, in oneembodiment the display 400 includes three groups of interferometricmodulators 401 having optical responses that, when the modulators 401are matched with the diffuser 402 as disclosed herein, correspond tored, green, and blue to produce a color display. In one such embodiment,the optical response of diffuser 402 may depend on the wavelength λ oflight passing through the diffuser 402. In one such embodiment, thediffuser 402 comprises a holographic optical element.

Variations in the design of the display are possible. For example, insome embodiments, a combination of several diffusers may be used toprovide a display with angular color shift at a selected angle that iswithin a predetermined tolerance. In another embodiment, one or morediffusers may be used to provide a color shift that is within apredetermined tolerance for two, three, or a range of angles. Stillother configurations are possible.

In one embodiment, an application of the interferometric modulator withdiffuser is to enable encryption or obscuring of the image of a displayto secure the image from unauthorized viewing. In one embodiment, thediffuser moves data from an invisible portion of the spectrum, e.g.,infrared, to a visible portion of the spectrum. The diffuser may bepositioned with respect to the interferometric modulator array so thatauthorized viewers receive light from the display through the diffuser.

Thus, in such an embodiment, the interferometric modulator produces anencrypted image and the diffuser is configured to decrypt the image. Inanother embodiment, the interferometric modulator array of the displayhas an optical response that is selected to receive input image data andproduce an output image that is difficult for the human eye to perceive,for example, in which colors are shifted such that the image isobscured. The diffuser is selected to shift the colors to a produce animage with colors indicative of the input image data.

While the above detailed description has shown, described and pointedout the fundamental novel features of the invention as applied tovarious embodiments, it will be understood that various omissions andsubstitutions and changes in the form and details of the systemillustrated may be made by those skilled in the art, without departingfrom the intent of the invention. The foregoing description detailscertain embodiments of the invention. It will be appreciated, however,that no matter how detailed the foregoing appears, the invention may beembodied in other specific forms without departing from its spirit oressential characteristics. The described embodiment is to be consideredin all respects only as illustrative and not restrictive.

1. A method of fabricating a display comprising: selecting a diffuserhaving an optical response; and disposing the diffuser in front of aninterferometric modulator array, the interferometric modulator arrayhaving an optical response that depends on angle of view, whereinselecting the diffuser comprises substantially matching the opticalresponse of the diffuser and the optical response of the interferometricmodulator array to reduce angular color shift with angle-of-view of thedisplay.
 2. The method of claim 1, wherein substantially matching theoptical response of the diffuser and the optical response of theinterferometric modulator array comprises determining the opticalresponse of the diffuser that with the optical response of theinterferometric modulator array produces a combined optical responsethat reduces angular color shift with angle-of-view of the display toless than a predetermined tolerance.
 3. The method of claim 2, whereinthe predetermined tolerance comprises a difference between a wavelengthof a peak intensity of the combined optical response produced at any twoangles of view within a predetermined range of angles of view.
 4. Themethod of claim 1, wherein the optical response of the at least oneinterferometric modulator has an intensity that depends at least in parton the angle of view and the wavelength of the incident light.
 5. Themethod of claim 1, wherein the optical response of the diffuser has anintensity that depends at least in part on angle of incidence of lightand on angle of view.
 6. The method of claim 5, wherein the opticalresponse of the diffuser further depends at least in part on thewavelength of light.
 7. A display fabricated by the method of claim 1.8. A method of tailoring optical properties of a display comprising aninterferometric modulator having a spectral responsivity and a diffuserhaving an optical response, the method comprising: selecting at leastone property of the diffuser with reference to the spectral responsivityof the interferometric modulator so as to reduce color shift of thedisplay.
 9. The method of claim 8, wherein selecting at least oneproperty of the diffuser comprises determining the optical response ofthe diffuser based on the spectral responsivity of the interferometricmodulator and a desired spectral responsivity of the display.
 10. Themethod of claim 9, wherein determining the optical response of thediffuser comprises calculating D(θ_(i), θ) by solving the equation,${R^{\prime}\left( {\theta,\lambda} \right)} = {\sum\limits_{\theta_{i}}{{D\left( {\theta_{i},\theta} \right)}{{R\left( {\theta_{i},\lambda} \right)}.}}}$11. The method of claim 8, wherein selecting at least one property ofthe diffuser comprises selecting variation in diffuser response withangle of view to be peaked at an angle other than the angle of incidenceof light incident on the diffuser.
 12. The method of claim 8, whereinselecting at least one property of the diffuser comprises selectingvariation in response with angle of view to be peaked at an angle otherthan θ=0°.
 13. The method of claim 8, further comprising selecting atleast one property of the interferometric modulator affecting thespectral responsivity.
 14. The method of claim 13, wherein selecting theat least one property of the diffuser comprises selecting the at leastone property of the diffuser with reference to the spectral responsivityof the interferometric modulator so as to reduce the color shift of thedisplay to less than a predetermined target value.
 15. The method ofclaim 8, wherein selecting at least one property of the diffusercomprises selecting material properties of the diffuser.
 16. The methodof claim 8, wherein the color shift is a difference in wavelengthbetween spectral lines in a spectral responsivity for the display whenfrom viewed any two of a range of angles.
 17. The method of claim 16,wherein the range of angles is between about −40 degrees and 40 degreeswith respect to an optical axis through the display and the color shiftis reduced to between about 5 and 30 nm for said range of angles.
 18. Amethod of limiting view of a display to authorized viewers, the methodcomprising: selecting at least one interferometric modulator having aspectral responsivity that depends at least in part on angle of view ofthe display; reflecting light indicative of an image from the at leastone interferometric modulator, the at least one interferometricmodulator being configured to at least partially obscure the image fromview; and diffusing the reflected light from the at least oneinterferometric modulator with a diffuser having an optical response,wherein the optical response of the diffuser is configured to so as todecrypt the image.
 19. The system of claim 18, wherein a spectralresponsivity for the display is produced that is shifted more toward thevisible wavelengths than the spectral responsivity of the at least oneinterferometric modulator.